#define _CRT_SECURE_NO_WARNINGS
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <functional>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii;
typedef long long ll; typedef vector<long long> vl; typedef pair<long long, long long> pll; typedef vector<pair<long long, long long> > vpll;
typedef vector<string> vs; typedef long double ld;
template<typename T, typename U> inline void amin(T &x, U y) { if (y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if (x < y) x = y; }


struct Xor128 {
	unsigned x, y, z, w;
	Xor128(): x(123456789), y(362436069), z(521288629), w(88675123) { }
	unsigned next() {
		unsigned t = x ^ (x << 11);
		x = y; y = z; z = w;
		return w = w ^ (w >> 19) ^ (t ^ (t >> 8));
	}
	//手抜き
	inline unsigned next(unsigned n) { return next() % n; }
};

//bottom upなTreap
//脱再帰！
//randomized binary searchにするにはchoiceRandomlyを
//	bool choiceRandomly(Ref l, Ref r) { return rng.next(l->size + r->size) < l->size; }
//に書き換えるだけでよい。
template<typename Node>
struct BottomupTreap {
	Xor128 rng;
	typedef Node *Ref;
	static int size(Ref t) { return !t ? 0 : t->size; }

	unsigned nextRand() { return rng.next(); }
private:
	bool choiceRandomly(Ref l, Ref r) {
		return l->priority < r->priority;
	}
public:

	Ref join(Ref l, Ref r) {
		if(!l) return r;
		if(!r) return l;

		Ref t = NULL;
		unsigned long long dirs = 0;
		int h;
		for(h = 0; ; ++ h) {
			if(h >= sizeof(dirs)*8 - 2) {
				//dirsのオーバーフローを防ぐために再帰する。
				//あくまでセーフティガードなのでバランスは多少崩れるかもしれない
				t = join(l->right, r->left);
				dirs = dirs << 2 | 1;
				h ++;
				break;
			}
			dirs <<= 1;
			if(choiceRandomly(l, r)) {
				Ref c = l->right;
				if(!c) {
					t = r;
					r = r->parent;
					break;
				}
				l = c;
			}else {
				dirs |= 1;
				Ref c = r->left;
				if(!c) {
					t = l;
					l = l->parent;
					break;
				}
				r = c;
			}
		}
		for(; h >= 0; -- h) {
			if(!(dirs & 1)) {
				Ref p = l->parent;
				t = l->linkr(t);
				l = p;
			}else {
				Ref p = r->parent;
				t = r->linkl(t);
				r = p;
			}
			dirs >>= 1;
		}
		return t;
	}

	typedef std::pair<Ref,Ref> RefPair;

	//l＜t≦rの(l,r)に分割する
	RefPair split2(Ref t) {
		Ref p, l = t->left, r = t;
		Node::cut(l); t->linkl(NULL);
		while(p = t->parent) {
			t->parent = NULL;
			if(p->left == t)
				r = p->linkl(r);
			else
				l = p->linkr(l);
			t = p;
		}
		return RefPair(l, r);
	}
	//l＜t＜rの(l,t,r)に分割する。(l,r)を返す
	RefPair split3(Ref t) {
		Ref p, l = t->left, r = t->right;
		Node::cut(l), Node::cut(r);
		t->linklr(NULL, NULL);
		while(p = t->parent) {
			t->parent = NULL;
			if(p->left == t)
				r = p->linkl(r);
			else
				l = p->linkr(l);
			t = p;
		}
		return RefPair(l, r);
	}
	Ref cons(Ref h, Ref t) {
		assert(size(h) == 1);
		if(!t) return h;
		Ref u = NULL;
		while(true) {
			if(choiceRandomly(h, t)) {
				Ref p = t->parent;
				u = h->linkr(t);
				t = p;
				break;
			}
			Ref l = t->left;
			if(!l) {
				u = h;
				break;
			}
			t = l;
		}
		while(t) {
			u = t->linkl(u);
			t = t->parent;
		}
		return u;
	}
};

//free treeのために、辺を基本として扱う
class EulerTourTreeWithMarks {
	struct Node {
		typedef BottomupTreap<Node> BST;

		Node *left, *right, *parent;
		int size;
		unsigned priority;
		char marks, markUnions;	//0ビット目がedgeMark, 1ビット目がvertexMark

		Node(): left(NULL), right(NULL), parent(NULL),
			size(1), priority(0), marks(0), markUnions(0) { }

		inline Node *update() {
			int size_t = 1, markUnions_t = marks;
			if(left) {
				size_t += left->size;
				markUnions_t |= left->markUnions;
			}
			if(right) {
				size_t += right->size;
				markUnions_t |= right->markUnions;
			}
			size = size_t, markUnions = markUnions_t;
			return this;
		}

		inline Node *linkl(Node *c) {
			if(left = c) c->parent = this;
			return update();
		}
		inline Node *linkr(Node *c) {
			if(right = c) c->parent = this;
			return update();
		}
		inline Node *linklr(Node *l, Node *r) {
			if(left = l) l->parent = this;
			if(right = r) r->parent = this;
			return update();
		}
		static Node *cut(Node *t) {
			if(t) t->parent = NULL;
			return t;
		}

		static const Node *findRoot(const Node *t) {
			while(t->parent) t = t->parent;
			return t;
		}
		static std::pair<Node*,int> getPosition(Node *t) {
			int k = BST::size(t->left);
			Node *p;
			while(p = t->parent) {
				if(p->right == t)
					k += BST::size(p->left) + 1;
				t = p;
			}
			return std::make_pair(t, k);
		}
		static const Node *findHead(const Node *t) {
			while(t->left) t = t->left;
			return t;
		}
		static void updatePath(Node *t) {
			while(t) {
				t->update();
				t = t->parent;
			}
		}
		static int getPosition(const Node *t) {
			int k = t->left ? t->left->size : 0;
			while(1) {
				const Node *p = t->parent;
				if(!p) return k;
				if(p->right == t)
					k += (p->left ? p->left->size : 0) + 1;
				t = p;
			}
		}
	};

	typedef Node::BST BST;
	BST bst;

	std::vector<Node> nodes;
	//各頂点に対してその頂点から出ているarcを1つだけ代表として持つ(無い場合は-1)
	//逆にarcに対して対応する頂点はたかだか1つである
	std::vector<int> firstArc;
	//辺・頂点に対する属性
	std::vector<bool> edgeMark, vertexMark;

	inline int getArcIndex(const Node *a) const { return a - &nodes[0]; }

	inline int arc1(int ei) const { return ei; }
	inline int arc2(int ei) const { return ei + (numVertices() - 1); }

public:
	inline int numVertices() const { return firstArc.size(); }
	inline int numEdges() const { return numVertices() - 1; }

	inline bool getEdgeMark(int a) const {
		return a < numEdges() ? edgeMark[a] : false;
	}
	inline bool getVertexMark(int v) const {
		return vertexMark[v];
	}
private:

	void updateMarks(int a, int v) {
		Node *t = &nodes[a];
		t->marks = getEdgeMark(a) << 0 | getVertexMark(v) << 1;
		Node::updatePath(t);
	}

	//firstArcの変更に応じて更新する
	void firstArcChanged(int v, int a, int b) {
		if(a != -1) updateMarks(a, v);
		if(b != -1) updateMarks(b, v);
	}

public:
	class TreeRef {
		friend class EulerTourTreeWithMarks;
		const Node *ref;
	public:
		TreeRef() { }
		TreeRef(const Node *ref_): ref(ref_) { }
		bool operator==(const TreeRef &that) const { return ref == that.ref; }
		bool operator!=(const TreeRef &that) const { return ref != that.ref; }
		bool isIsolatedVertex() const { return ref == NULL; }
	};

	void init(int N) {
		int M = N - 1;
		firstArc.assign(N, -1);
		nodes.assign(M * 2, Node());
		for(int i = 0; i < M * 2; i ++)
			nodes[i].priority = bst.nextRand();
		edgeMark.assign(M, false);
		vertexMark.assign(N, false);
	}

	TreeRef getTreeRef(int v) const {
		int a = firstArc[v];
		return TreeRef(a == -1 ? NULL : Node::findRoot(&nodes[a]));
	}

	bool isConnected(int v, int w) const {
		if(v == w) return true;
		int a = firstArc[v], b = firstArc[w];
		if(a == -1 || b == -1) return false;
		return Node::findRoot(&nodes[a]) == Node::findRoot(&nodes[b]);
	}

	int getTreeFirstArc(TreeRef t) const {
		assert(!t.isIsolatedVertex());
		return getArcIndex(t.ref);
	}

	static int getSize(TreeRef t) {
		if(t.isIsolatedVertex()) return 1;
		else return t.ref->size / 2 + 1;
	}

	int getPosition(int v) const {
		int a = firstArc[v];
		if(a == -1) return 0;
		return Node::getPosition(&nodes[a]);
	}

	void link(int ti, int v, int w) {
		int a1 = arc1(ti), a2 = arc2(ti);
		//v→wがa1に対応するようにする
		if(v > w) std::swap(a1, a2);

		int va = firstArc[v], wa = firstArc[w];

		Node *l, *m, *r;
		if(va != -1) {
			//evert。順番を入れ替えるだけ
			std::pair<Node*,Node*> p = bst.split2(&nodes[va]);
			m = bst.join(p.second, p.first);
		}else {
			//vが孤立点の場合
			m = NULL;
			firstArc[v] = a1;
			firstArcChanged(v, -1, a1);
		}
		if(wa != -1) {
			std::pair<Node*,Node*> p = bst.split2(&nodes[wa]);
			l = p.first, r = p.second;
		}else {
			//wが孤立点の場合
			l = r = NULL;
			firstArc[w] = a2;
			firstArcChanged(w, -1, a2);
		}
		//w→vの辺をmの先頭＝lの末尾にinsert
		m = bst.cons(&nodes[a2], m);
		//v→wの辺をmの末尾＝rの先頭にinsert
		r = bst.cons(&nodes[a1], r);

		bst.join(bst.join(l, m), r);
	}

	void cut(int ti, int v, int w) {
		//v→wがa1に対応するようにする
		if(v > w) std::swap(v, w);

		int a1 = arc1(ti), a2 = arc2(ti);
		std::pair<Node*,Node*> p = bst.split3(&nodes[a1]);
		int prsize = BST::size(p.second);
		std::pair<Node*,Node*> q = bst.split3(&nodes[a2]);
		Node *l, *m, *r;
		//a1,a2の順番を判定する。a1＜a2ならp.secondが変わっているはず
		if(p.second == &nodes[a2] || BST::size(p.second) != prsize) {
			l = p.first, m = q.first, r = q.second;
		}else {
			//a2＜a1の順番である。v→wの辺がa1であって親→子であることにする
			std::swap(v, w);
			std::swap(a1, a2);
			l = q.first, m = q.second, r = p.second;
		}

		//firstArcを必要に応じて書き換える
		if(firstArc[v] == a1) {
			int b;
			if(r != NULL) {
				//vが根じゃないなら右側の最初の辺でよい
				b = getArcIndex(Node::findHead(r));
			}else {
				//vが根なら最初の辺でよい。孤立点になるなら-1
				b = !l ? -1 : getArcIndex(Node::findHead(l));
			}
			firstArc[v] = b;
			firstArcChanged(v, a1, b);
		}
		if(firstArc[w] == a2) {
			//wが根になるので最初の辺でよい。孤立点になるなら-1
			int b = !m ? -1 : getArcIndex(Node::findHead(m));
			firstArc[w] = b;
			firstArcChanged(w, a2, b);
		}

		bst.join(l, r);
	}

	void changeEdgeMark(int ti, bool b) {
		assert(ti < numEdges());
		edgeMark[ti] = b;
		Node *t = &nodes[ti];
		t->marks = (b << 0) | (t->marks & (1 << 1));
		Node::updatePath(t);
	}
	void changeVertexMark(int v, bool b) {
		vertexMark[v] = b;
		int a = firstArc[v];
		if(a != -1) {
			Node *t = &nodes[a];
			t->marks = (t->marks & (1 << 0)) | (b << 1);
			Node::updatePath(t);
		}
	}

	template<typename Callback>
	bool enumMarkedEdges(TreeRef tree, Callback callback) const {
		return enumMarks<0,Callback>(tree, callback);
	}
	//孤立点の場合は呼び側でその頂点だけ処理する必要がある
	template<typename Callback>
	bool enumMarkedVertices(TreeRef tree, Callback callback) const {
		return enumMarks<1,Callback>(tree, callback);
	}
private:
	//callback : TreeEdgeIndex×2 -> Bool
	//引数は頂点をそこからのincident arcで示し、"(正方向 ? 0 : N-1) + treeEdgeIndex"を表す。方向はv,wの大小で処理すればよい
	//callbackは継続するかどうかをboolで返す。最後まで列挙し終えたかどうかを返す。
	template<int Mark, typename Callback>
	bool enumMarks(TreeRef tree, Callback callback) const {
		if(tree.isIsolatedVertex()) return true;
		const Node *t = tree.ref;
		if(t->markUnions >> Mark & 1)
			return enumMarksRec<Mark,Callback>(t, callback);
		else
			return true;
	}

	//平衡木なので深さは深くないので再帰して問題ない
	template<int Mark, typename Callback>
	bool enumMarksRec(const Node *t, Callback callback) const {
		const Node *l = t->left, *r = t->right;
		if(l && (l->markUnions >> Mark & 1))
			if(!enumMarksRec<Mark,Callback>(l, callback)) return false;
		if(t->marks >> Mark & 1)
			if(!callback(getArcIndex(t))) return false;
		if(r && (r->markUnions >> Mark & 1))
			if(!enumMarksRec<Mark,Callback>(r, callback)) return false;
		return true;
	}

public:
	//デバッグ用
	void debugEnumEdges(std::vector<int> &out_v) const {
		int M = numEdges();
		for(int ti = 0; ti < M; ti ++) {
			const Node *t = &nodes[ti];
			if(t->left || t->right || t->parent)
				out_v.push_back(ti);
		}
	}
};

//treeEdgeにはそれぞれ0～N-1のインデックスが与えられる。これは全てのレベルで共通。
//ところで"level up"って和製英語なんだ。promoteでいいかな。
//Sampling heuristic ランダムケースで超速く(4倍とか)なったんだけど！いいね！
class HolmDeLichtenbergThorup {
	typedef HolmDeLichtenbergThorup This;
	typedef EulerTourTreeWithMarks Forest;
	typedef Forest::TreeRef TreeRef;

	int numVertices_m;
	int numSamplings;

	//DynamicTreeはコピーできないけどまあその状態で使わなきゃいいじゃんということで…
	std::vector<Forest> forests;

	std::vector<char> edgeLevel;
	std::vector<int> treeEdgeIndex;	// : EdgeIndex -> TreeEdgeIndex
	std::vector<int> treeEdgeMap;	// : TreeEdgeIndex -> EdgeIndex
	std::vector<int> treeEdgeIndexFreeList;	// : [TreeEdgeIndex]

	//arcも方向はEulerTourTreeと同じようにv,wの大小に合わせる
	std::vector<int> arcHead;

	std::vector<std::vector<int> > firstIncidentArc;
	std::vector<int> nextIncidentArc, prevIncidentArc;

	//一時的に使う。使い回して使う
	std::vector<bool> edgeVisited;
	std::vector<int> visitedEdges;	// : [EdgeIndex | TreeEdgeIndex]

	int arc1(int ei) const { return ei; }
	int arc2(int ei) const { return numMaxEdges() + ei; }
	int arcEdge(int i) const { return i >= numMaxEdges() ? i - numMaxEdges() : i; }

	bool replace(int lv, int v, int w) {
		Forest &forest = forests[lv];

		TreeRef vRoot = forest.getTreeRef(v), wRoot = forest.getTreeRef(w);
		assert(vRoot.isIsolatedVertex() || wRoot.isIsolatedVertex() || vRoot != wRoot);

		int vSize = forest.getSize(vRoot), wSize = forest.getSize(wRoot);

		int u; TreeRef uRoot; int uSize;
		if(vSize <= wSize)
			u = v, uRoot = vRoot, uSize = vSize;
		else
			u = w, uRoot = wRoot, uSize = wSize;

		//replacement edgeを探す
		int replacementEdge = -1;
		enumIncidentArcs(forest, uRoot, u, lv, FindReplacementEdge(uRoot, &replacementEdge));

		//"Sampling heuristic"
		//早い時点で見つかったならT_u,他のincident arcsをレベルアップさせなくても計算量的に問題ない
		if(replacementEdge != -1 && (int)visitedEdges.size() + 1 <= numSamplings) {
			//replacementEdgeを処理する
			deleteNontreeEdge(replacementEdge);
			addTreeEdge(replacementEdge);
			for(int i = 0; i < (int)visitedEdges.size(); i ++)
				edgeVisited[visitedEdges[i]] = false;
			visitedEdges.clear();
			return true;
		}
		
		//見つけたincident arcsを一斉にレベルアップさせる。edgeVisitedの後処理もする
		for(int i = 0; i < (int)visitedEdges.size(); i ++) {
			int ei = visitedEdges[i];
			edgeVisited[ei] = false;

			deleteNontreeEdge(ei);

			++ edgeLevel[ei];

			insertNontreeEdge(ei);
		}
		visitedEdges.clear();

		//このレベルのT_uの辺を列挙する
		forest.enumMarkedEdges(uRoot, EnumLevelTreeEdges(this));
		//列挙したT_uの辺を一斉にレベルアップさせる
		for(int i = 0; i < (int)visitedEdges.size(); i ++) {
			int ti = visitedEdges[i];

			int ei = treeEdgeMap[ti];
			int v = arcHead[arc2(ei)], w = arcHead[arc1(ei)];
			int lv = edgeLevel[ei];

			edgeLevel[ei] = lv + 1;

			forests[lv].changeEdgeMark(ti, false);
			forests[lv+1].changeEdgeMark(ti, true);

			forests[lv+1].link(ti, v, w);
		}
		visitedEdges.clear();

		if(replacementEdge != -1) {
			//T_uの辺列挙の前に構造が変わると困るのでreplacementEdgeはこのタイミングで処理する
			deleteNontreeEdge(replacementEdge);
			addTreeEdge(replacementEdge);
			return true;
		}else if(lv > 0) {
			return replace(lv-1, v, w);
		}else {
			return false;
		}
	}

	struct EnumLevelTreeEdges {
		This *thisp;
		EnumLevelTreeEdges(This *thisp_): thisp(thisp_) { }

		inline bool operator()(int a) {
			thisp->enumLevelTreeEdges(a);
			return true;
		}
	};
	void enumLevelTreeEdges(int ti) {
		visitedEdges.push_back(ti);
	}

	//孤立点の時特別な処理をするなどしなければいけないのでヘルパー
	template<typename Callback>
	bool enumIncidentArcs(Forest &forest, TreeRef t, int u, int lv, Callback callback) {
		if(t.isIsolatedVertex())
			return enumIncidentArcsWithVertex<Callback>(lv, u, callback);
		else
			return forest.enumMarkedVertices(t, EnumIncidentArcs<Callback>(this, lv, callback));
	}

	template<typename Callback>
	struct EnumIncidentArcs {
		This *thisp;
		int lv;
		Callback callback;

		EnumIncidentArcs(This *thisp_, int lv_, Callback callback_):
			thisp(thisp_), lv(lv_), callback(callback_) { }

		inline bool operator()(int tii) const {
			return thisp->enumIncidentArcsWithTreeArc(tii, lv, callback);
		}
	};

	template<typename Callback>
	bool enumIncidentArcsWithTreeArc(int tii, int lv, Callback callback) {
		int u = getTreeEdgeIndexTailVertex(tii);
		return enumIncidentArcsWithVertex(lv, u, callback);
	}

	int getTreeEdgeIndexTailVertex(int tii) const {
		bool dir = tii >= numVertices() - 1;
		int ti = dir ? tii - (numVertices() - 1) : tii;
		int ei = treeEdgeMap[ti];
		int v = arcHead[arc2(ei)], w = arcHead[arc1(ei)];
		//方向を求め、そのarcのtailの頂点を取得する
		int u = !(dir != (v > w)) ? v : w;
		return u;
	}

	//1つの頂点を処理する
	template<typename Callback>
	bool enumIncidentArcsWithVertex(int lv, int u, Callback callback) {
		int it = firstIncidentArc[lv][u];
		while(it != -1) {
			if(!callback(this, it))
				return false;
			it = nextIncidentArc[it];
		}
		return true;
	}

	struct FindReplacementEdge {
		TreeRef uRoot;
		int *replacementEdge;
		FindReplacementEdge(TreeRef uRoot_, int *replacementEdge_):
			uRoot(uRoot_), replacementEdge(replacementEdge_) { }

		inline bool operator()(This *thisp, int a) const {
			return thisp->findReplacementEdge(a, uRoot, replacementEdge);
		}
	};

	//1つのarcを処理する
	bool findReplacementEdge(int a, TreeRef uRoot, int *replacementEdge) {
		int ei = arcEdge(a);
		if(edgeVisited[ei]) return true;

		int lv = edgeLevel[ei];
		TreeRef hRoot = forests[lv].getTreeRef(arcHead[a]);
		
		if(hRoot.isIsolatedVertex() || hRoot != uRoot) {
			//別の木に渡されているならreplacement edgeである。
			*replacementEdge = ei;
			return false;
		}
		//replacement edgeはvisitedEdgesに入れたくないのでこの位置でマークする
		edgeVisited[ei] = true;
		visitedEdges.push_back(ei);
		return true;
	}

	void addTreeEdge(int ei) {
		int v = arcHead[arc2(ei)], w = arcHead[arc1(ei)];
		int lv = edgeLevel[ei];

		int ti = treeEdgeIndexFreeList.back();
		treeEdgeIndexFreeList.pop_back();
		treeEdgeIndex[ei] = ti;
		treeEdgeMap[ti] = ei;

		forests[lv].changeEdgeMark(ti, true);

		for(int i = 0; i <= lv; i ++)
			forests[i].link(ti, v, w);
	}

	void insertIncidentArc(int a, int v) {
		int ei = arcEdge(a);
		int lv = edgeLevel[ei];
		assert(treeEdgeIndex[ei] == -1);

		int next = firstIncidentArc[lv][v];
		firstIncidentArc[lv][v] = a;
		nextIncidentArc[a] = next;
		prevIncidentArc[a] = -1;
		if(next != -1) prevIncidentArc[next] = a;

		if(next == -1)
			forests[lv].changeVertexMark(v, true);
	}

	void deleteIncidentArc(int a, int v) {
		int ei = arcEdge(a);
		int lv = edgeLevel[ei];
		assert(treeEdgeIndex[ei] == -1);

		int next = nextIncidentArc[a], prev = prevIncidentArc[a];
		nextIncidentArc[a] = prevIncidentArc[a] = -2;

		if(next != -1) prevIncidentArc[next] = prev;
		if(prev != -1) nextIncidentArc[prev] = next;
		else firstIncidentArc[lv][v] = next;

		if(next == -1 && prev == -1)
			forests[lv].changeVertexMark(v, false);
	}

	void insertNontreeEdge(int ei) {
		int a1 = arc1(ei), a2 = arc2(ei);
		insertIncidentArc(a1, arcHead[a2]);
		insertIncidentArc(a2, arcHead[a1]);
	}

	void deleteNontreeEdge(int ei) {
		int a1 = arc1(ei), a2 = arc2(ei);
		deleteIncidentArc(a1, arcHead[a2]);
		deleteIncidentArc(a2, arcHead[a1]);
	}

public:
	HolmDeLichtenbergThorup(): numVertices_m(0), numSamplings(0) { }

	int numVertices() const { return numVertices_m; }
	int numMaxEdges() const { return edgeLevel.size(); }

	void init(int N, int M) {
		numVertices_m = N;

		int levels = 1;
		while(1 << levels <= N / 2) levels ++;

		//サンプリング数を設定する。適切な値はよくわからない
		numSamplings = (int)(levels * 1);

		forests.resize(levels);
		for(int lv = 0; lv < levels; lv ++)
			forests[lv].init(N);

		edgeLevel.assign(M, -1);

		treeEdgeIndex.assign(M, -1);
		treeEdgeMap.assign(N - 1, -1);

		treeEdgeIndexFreeList.resize(N-1);
		for(int ti = 0; ti < N-1; ti ++)
			treeEdgeIndexFreeList[ti] = ti;

		arcHead.assign(M * 2, -1);

		firstIncidentArc.resize(levels);
		for(int lv = 0; lv < levels; lv ++)
			firstIncidentArc[lv].assign(N, -1);
		nextIncidentArc.assign(M * 2, -2);
		prevIncidentArc.assign(M * 2, -2);

		edgeVisited.assign(M, false);
	}

	bool insertEdge(int ei, int v, int w) {
		assert(0 <= ei && ei < numMaxEdges() && 0 <= v && v < numVertices() && 0 <= w && w < numVertices());
		assert(edgeLevel[ei] == -1);

		int a1 = arc1(ei), a2 = arc2(ei);
		arcHead[a1] = w, arcHead[a2] = v;

		bool treeEdge = !forests[0].isConnected(v, w);

		edgeLevel[ei] = 0;
		if(treeEdge) {
			addTreeEdge(ei);
		}else {
			treeEdgeIndex[ei] = -1;
			//ループは見たくないのでリストにも入れない
			if(v != w)
				insertNontreeEdge(ei);
		}

		return treeEdge;
	}

	bool deleteEdge(int ei) {
		assert(0 <= ei && ei < numMaxEdges() && edgeLevel[ei] != -1);

		int a1 = arc1(ei), a2 = arc2(ei);
		int v = arcHead[a2], w = arcHead[a1];

		int lv = edgeLevel[ei];
		int ti = treeEdgeIndex[ei];

		bool splitted = false;
		if(ti != -1) {
			treeEdgeMap[ti] = -1;
			treeEdgeIndex[ei] = -1;
			treeEdgeIndexFreeList.push_back(ti);

			for(int i = 0; i <= lv; i ++)
				forests[i].cut(ti, v, w);

			forests[lv].changeEdgeMark(ti, false);

			splitted = !replace(lv, v, w);
		}else {
			//ループはリストに入ってない
			if(v != w)
				deleteNontreeEdge(ei);
		}

		arcHead[a1] = arcHead[a2] = -1;
		edgeLevel[ei] = -1;

		return splitted;
	}

	bool isConnected(int v, int w) const {
		return forests[0].isConnected(v, w);
	}

	int findComponentRepresent(int v) const {
		assert(0 <= v && v < numVertices());
		TreeRef t = forests[0].getTreeRef(v);
		if(t.isIsolatedVertex()) {
			return v;
		}else {
			int tii = forests[0].getTreeFirstArc(t);
			return getTreeEdgeIndexTailVertex(tii);
		}
	}

	bool getParity(int v) const {
		return forests[0].getPosition(v) % 2 != 0;
	}

	void dbgForestO(std::ostream &o) const {
		int N = numVertices(), M = numMaxEdges();
		int levels = forests.size();
		std::vector<bool> visited(M, false);
		o << "graph {\n";
		for(int lv = 0; lv < levels; lv ++) {
			o << "subgraph cluster_" << lv << "{\n";
			o << "label = " << '"' << "level " << lv << '"' << ";\n";
			for(int u = 0; u < N; u ++) {
				o << '"' << lv << "_" << u << '"';
				o << "[label=" << u << "];\n";

				int it = firstIncidentArc[lv][u];
				while(it != -1) {
					int ei = arcEdge(it);
					if(!visited[ei]) {
						visited[ei] = true;
						int v = arcHead[arc2(ei)], w = arcHead[arc1(ei)];
						o << '"' << lv << "_" << v << '"' << " -- " << '"' << lv << "_" << w << '"';
						o << " [style=dotted]" << ";\n";
					}
					it = nextIncidentArc[it];
				}
			}
			std::vector<int> edges;
			forests[lv].debugEnumEdges(edges);
			for(int i = 0; i < (int)edges.size(); i ++) {
				int ti = edges[i];
				int ei = treeEdgeMap[ti];
				assert(ei != -1);
				int lvi = edgeLevel[ei];
				int a1 = arc1(ei), a2 = arc2(ei);
				int v = arcHead[a2], w = arcHead[a1];
				o << '"' << lv << "_" << v << '"' << " -- " << '"' << lv << "_" << w << '"';
//				o << " [style=" << (lvi == lv ? "solid" : "dashed") << "]";
				o << ";\n";
			}
			o << "}\n";
		}
		o << "}" << std::endl;
	}
};

vector<int> sqrtSort(const vector<pair<int,int> > &q, const int S) {
	int n = q.size();
	vector<long long> pack(n);
	for(int i = 0; i < n; i ++) {
		pack[i] =
			(long long)(q[i].first/S) << 50 |
			(long long)((q[i].first/S & 1) == 0 ? q[i].second : (1<<25) - 1 - q[i].second) << 25 |
			i;
	}
	sort(all(pack));
	vector<int> res(n);
	for(int i = 0; i < n; i ++)
		res[i] = pack[i] & ((1 << 25) - 1);
	return res;
}

int main() {
	int n, m, q;
	scanf("%d%d%d", &n, &m, &q);
	vpii edges(m);
	rep(i, m) {
		int x, y;
		scanf("%d%d", &x, &y), -- x, -- y;
		edges[i] = mp(x, y);
	}
	cerr << endl;
	vector<int> maximal(m+1, -1);
	HolmDeLichtenbergThorup hdt;
	hdt.init(n, m);
	int right = 0;
	rep(left, m+1) {
		while(right < m) {
			int ei = right;
			pii p = edges[ei];
			int x = p.first, y = p.second;
			if(hdt.isConnected(x, y)) {
//				hdt.dbgForestO(cerr);
//				cerr << left << ", "<< right << ", " << x << ", "<< y << ": " << hdt.getParity(x) << ", " << hdt.getParity(y) << endl;
				if(hdt.getParity(x) == hdt.getParity(y))
					break;
			}
			hdt.insertEdge(ei, x, y);
			++ right;
		}
//		cerr << left << ": " << right << endl;
		maximal[left] = right;
		if(left == m) break;
		int ei = left;
		hdt.deleteEdge(ei);
	}

	rep(i, q) {
		int l, r;
		scanf("%d%d", &l, &r), -- l;
		bool ans = maximal[l] >= r;
		puts(ans ? "Possible" : "Impossible");
	}

	return 0;
}